Nuprl Lemma : num-antecedents-fun_exp
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[Sys:EClass(Top)]. ∀[f:sys-antecedent(es;Sys)]. ∀[n:ℕ]. ∀[e:E(Sys)].
#f(f^n e) = (#f(e) - n) ∈ ℤ supposing n ≤ #f(e)
Proof
Definitions occuring in Statement :
num-antecedents: #f(e),
sys-antecedent: sys-antecedent(es;Sys),
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
fun_exp: f^n,
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
le: A ≤ B,
apply: f a,
subtract: n - m,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
all: ∀x:A. B[x],
top: Top,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
num-antecedents: #f(e),
sys-antecedent: sys-antecedent(es;Sys),
es-E-interface: E(X),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
squash: ↓T,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[Sys:EClass(Top)]. \mforall{}[f:sys-antecedent(es;Sys)]. \mforall{}[n:\mBbbN{}]. \mforall{}[e:E(Sys)].
\#f(f\^{}n e) = (\#f(e) - n) supposing n \mleq{} \#f(e)
Date html generated:
2016_05_16-PM-02_48_42
Last ObjectModification:
2016_01_17-PM-07_30_29
Theory : event-ordering
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